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There existsa negotiated settlement that is pareto optimal:
:<math>u_A(x) > p- c_A\,</math>
is strictly preferred to fighting. Risk aversion will increase the range. This range exists because bargaining is ex-post inefficient.
 
Proof: Choose an <math>\epsilon</math> such that <math>0<\epsilon<\min\{c_{A},c_{B}\}</math>. Let <math>a=\max\{0,p-\epsilon\}</math>, <math>b=\min\{p+\epsilon,1\}</math>. Consider <math>x'\in[a,b]</math> by weak concavity, <math>u_{A}(x')\geq x'</math>. Further <math>x'>p-c_{A}</math>, so it is better than war, because <math>x'\geq a \geq p-\epsilon \geq p- c_{A}</math>. Can make same argument for B.
#The leaders are risk neutral or risk averse. This is a reasonable assumption: A risk-acceptant leader is analogous to a compulsive gambler, that has the expected outcome of eliminating both the state and the regime.
#A continous range of settlement exists, to allow for feasible outcomes that lie in the range. But even without this, continuous side-payments would offer a solution, or randomization/alternation (c.f time-sharing!) would allow for negotiated outcomes. Though sharing a throne might be problematic.
 
==Private Information and Incentives to Misrepresent==
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